BASIC PROPERTIES OF INTEGRATION THTEGRATG THE FOILOWING stan2% Sec' 2xdx 2. 7) ァメuIS× COSX

Q: If F (t) = L¯* {?+10s+34 2s+10 s2+10s+34 1nd F (T) O 2e3 -2e-37 2e5 2e-5T

A: As we know that, The property for the inverse Laplace transformation; If L-1Fs=ft then L-1Fs-a=eatft...

Q: L{(1+t")e*3t}=

A:

Q: Given the equation S'sin x cos x dx The equation can be answered using Lesson No. 5(Case 2) and usin...

A:

Q: 4. Brian wishes his son to receive P500,000.00 twenty years from now. What amount should he invest i...

A: Brain wishes fis son to receive P500,000.00 twenty years from now.

Q: d*y The equation da4 4y 1+ ( is 72 dx O linear and ordinary O linear and partial O nonlinear and ord...

A: Here we have to find the type of given differential equation.

Q: The Laplace transform of th is valid for O s>n O s>0

A: The Laplace transform of tn is        Ltn=n!sn+1, for s>0

Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y y =...

A: Given:    f(x) = 7x(x-2)2

Q: d'y Given the differential equation, dx? dy 2y = e2" sin(2x) cos(2x), the propsec - dæ particular so...

A:

Q: Sesame seeds are often used as a garnish in Asian dishes. However, they need to be toasted at 350°F ...

A:

Q: cos(2æ) Given the differential equation y" + 4y' + 5y = Propose an appropriate particular solution. ...

A:

Q: 2.4 2.5 2.6 2.7 2.8 1248 1571 1977 2489 3132 Estimate h' (2.6) using the table above. h'(2.6)

A: First order central difference algorithm approximate the First order derivative using formula       ...

Q: Given the following graph, what is the corresponding function (t > 0)?

A: Follow the procedure given below.

Q: If the Laplace Transform of F (t) = /t3 is 4s 2 what is the Laplace Transform of F (t) = e' Vt3? 4(s...

A:

Q: lim (4.x – 3) = 9

A: The given limit,      limx→34x-3=9

Q: For the following differential equation, (3D4 – 3D² – 3D + 6) y = 0, how many - arbitrary constants ...

A:

Q: The equation of a curve is y = 4Vx+ Vx dy (i) Obtain an expression for dr (ii) A point is moving alo...

A:

Q: 34x The partial fraction decomposition of 8x2 can 10х + 3 f(x) 2х — 1 g(x) be written in the form of...

A:

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 34 cm to a length ...

A:  4 J of work is needed to stretch a spring from its natural length of 34 cm to a length of 48 cm. (a...

Q: s2+10s+34 2s+10 If F (t) = L-1{ find F (0) s2+10s+34 O -2 o 1 O-1 o 2 Previous Nez

A:

Q: Given the following graph, what is the corresponding function (t 0)? 1 1 O y =t – tu (t – 1) + 2 u (...

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

Q: -6e' sin(at – 3) dt

A:

Q: What is the result when you square a binomial?

A: When square a binomial

Q: Show that (4, 5) is on the graph of f(x) = 2x + 1. Since f(4) = 5 the point (4, 5) is on f(x). %3D F...

A:

Q: Find the Laplace Transform of the piecewise function. (2 ,0<t<4; w(t) = { í 1? ,t 4. O 252+e-48 (2+8...

A:

Q: For the integral dr x+4 (a) Find the average value of f on [0, 5]. (b) Find a number z that satisfie...

A:

Q: lim x-->3 f(x)=8 and lim x--->3 g(x)= -4 1) limx--->3 (3f(x)-5g(x)) 2) lim x---> G(x)^3 + 50 /  ( ...

A:

Q: Given the following graph, what is the corresponding function (t > 0)?

A: From the given graph ,what is corresponding function 

Q: Which of the following is equivalent to the differential operator (D-9)(D+9)y? O (D² – 2D+ 81) y O (...

A: To determine:

Q: The definition of the error function also defines an "error term" E(1, y). Find E(x, y) for the func...

A: We need to find error function.

Q: oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in ...

A:

Q: x+5 lim x→2 x´ – 4 x+5 lim x→2* x? – 4 x+5 lim 2 x→2 x² - 4

A: The given limits,limx→2-x+5x2-4limx→2+x+5x2-4limx→2x+5x2-4

Q: For the function

A: Given, f(x)=(2x-2)5   yes given function is a power function

Q: Find the approximations T, M and S, for n = 6 and 12. Then compute the corresponding errors ET, EM, ...

A:

Q: Use numerical or graphical evidence to determine the left and right hand limits of the function. |4 ...

A:    

Q: se the shell method to find the volume of the solid generated by revolving e shaded region about the...

A: Topic:- application of integration

Q: An automobile's velocity starting from rest is given by the equation below, where v is measured in f...

A: Given query is to find y the acceleration at different times where v(t) is velocity.

Q: aph. f(x) = 흑x 8 %3D 10 9 8 6 4 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 -1 3 4 5 6 9 2 7 10 -2 No solutio...

A: Given query is to graph the function using graphing tool.

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region...

A: Topic = Volume

Q: If F (t) = L-{a10 find F (7) 2s+10 82+10s+34 2e3 2e5m -2e-5m -2e-3T

A:

Q: A voltage source E=5V is connected in series to a capacitance of 1 x 10-6 farad and a resistance of ...

A:

Q: ind the general solution : a csc() – y] da + ædy = 0 X CSC x = e (csc + cot ) In (ese + cot ) In = c...

A:

Q: 31) Find tue derivetive of tue funcrion heae) = I Sinh 2x -7X 4

A: For derivatives we just apply differentiation both side. 

Q: 2х+9 1. limxo x-2 х-2 3x2+4 2. limx x³ –64 3. limxo x+25 x2 -81 x4+81 4. limx→-∞ х3—27 5. limx0 x³+2...

A:

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t³j ...

A: Given: - The function is, r(t)=ti+5tj+t2ku(t)=5ti+t2j+t3k To find: - The derivative of (2t)u(t),

Q: Differentiate each function with respect to x. 4. y = (-5x^3- 4)^3 -2)^5 5. y = ((-5x^3 -2)^4 -3)^3

A: Since we are given with the multiple number of question and answered according to the guideline.

Q: 2 dy + x da The differential equation g3. - 5y = e" is: %3D O linear and second-order O non-linear a...

A:

Q: d Use the table below to find [1.3g(x) dx x= 1 1 3 4 5 f'(x) g'(x) 1 3 2 4 3 2 5 1 4 d [1.3g(x)] dx ...

A: Simply differentiate and put all the values.

Q: 1. A committee of 5 shareholders is to be chosen from a larger group of 7 men and 5 women. How many ...

A: